Scale-up criteria

Dimensional Analysis. Dimensional analysis can be helpful in analyzing reactor performance and developing scale-up criteria. Seven dimensionless groups used in generalized rate equations for continuous flow reaction systems are Hsted in Table 4. Other dimensionless groups apply in specific situations (58—61). Compromising assumptions are often necessary, and their vaHdation must be estabHshed experimentally or by analogy to previously studied systems. 

Various chemical engineering scale-up criteria are available in the literature and have been met with greater of lesser success in the literature. Each is examined in detail below. 

The conventional scale-up criteria scale-up with constant stirrer speed , scale-up with constant tip speed and scale-up with constant specific energy input are all based on the assumption that only one mixing process is limiting. If, for example, the specific energy input is kept constant with scale-up, the same micromixing behaviour could be expected on different scales. The mesomixing time, however, will change with scale-up as a result, the kinetic rates and particle properties will be different and scale-up will fail. 

The design methods de.scribed above rely on correlations of the overall reactor average quantities obtained from experimental tanks of different scales. The most important deficiency of these methods is that local effects are not taken into consideration, while these might be responsible for the overall reactor performance. Accordingly, if none of the above scale-up criteria is found satisfactory (see e.g. data of Middleton et ai, 1986) a more fundamental approach must be applied, although not necessarily as complex as the one presented in Section 5.4.S.2. Such an approach was presented by Paul et al. (1971) who found that the yield of the desired intermediate in a system of consecutive reactions (iodination of L-tjrosine) correlates reasonably with fluctuations of the velocity, So, these fluctuations could be chosen as a criterion for scale-up of the reactor. The average value for u in the upper part of the tank was evaluated from ... 

TABLE 2.1. Scale-Up Criteria from the Viewpoint of Out-Sourcing Chemical Firms... 

However, it is difficult, if not impossible, to satisfy the dynamic similarity when more than one dimensionless group is involved in a system, which creates the needs of scale-up criteria. The following example addresses this problem. 

The previous example problem illustrates the difficulties involved in the scale-up of the findings of small-scale results. Therefore, we need to reduce the number of dimensionless parameters involved to as few as possible, and we also need to determine which is the most important parameter, so that we may set this parameter constant. However, even though only one dimensionless parameter may be involved, we may need to define the scale-up criteria. 

Although considerable studies on the use of centrifugal fields in chemical processing have been reported for lab- and pilot-scale operations, little information is public on scale-up criteria for either performance parameters or equipment design. Three examples of commercial use of centrifugal fields are available for review. These include liquid-liquid extraction, water deaeration, and reactive stripping for hypochlorous acid production. 

In the presence of significant thermal effects, one of the above-mentioned fluid dynamic scale-up criteria must be considered, together with the criterion US/V = constant, which can be made more realistic by considering that heat exchange surface S can be different from SL and by introducing a proper functional relationship for U. If the internal resistance to heat transfer prevails, U may be intended as the internal heat transfer coefficient h, so that the relationship... 

Since in animal cell culture processes the effects of mechanical stress are much more relevant than in microbial fermentations (Chisti, 1993), it is quite common to adopt scale-up criteria that are associated with cell damage (Joshi et al., 1996), such as constant peripheral impeller velocity, constant aeration rate, and constant integrated shear stress (Croughan et al., 1987). 

Different scale-up criteria and consequences Ratio of the value at 10 m3 relative to the value at 10 I... 

A differential equation describing the material balance around a section of the system was first derived, and the equation was made dimensionless by appropriate substitutions. Scale-up criteria were then established by evaluating the dimensionless groups. A mathematical model was further developed based on the kinetics of the reaction, describing the effect of the process variables on the conversion, yield, and catalyst activity. Kinetic parameters were determined by means of both analogue and digital computers. 

Jarmer DJ, Lengsfeld CS, Randolph TW. 2006. Scale-up criteria for an injector with a confined mixing chamber during precipitation with a compressed fluid antisolvent. J. Supercritical Fluids 37 242-253. 

According to these models, the turbulent field for chemical reaction is determined once Ls and e are known at any position in the reactor. This leads to interesting scale-up criteria in stirred reactors GO the mixing characteristics are the same if g/l is kept constant. As e v P/pV and V L, the power input P should be proportional to L Lg. This may be as high as if one assumes that Ls L. The empirical exponent actually lies in between 3 and 5. 

Table 7 lists these and a number of other scale-up criteria for stirred tanks. Here it is assumed that the fluid is the same on scale up, i.e. density and viscosity are both constant, and that the vessel is operating in the fully turbulent, constant power number regime. 

Table 7 Some scale-up criteria for geometrically similar stirred vessels in the fully turbulent regime12...

However, by examining the adsorption behavior of polypeptides and proteins with comparable porous and nonporous particles in finite baths, packed columns and expanded or fluidized beds, an iterative simulation approach based on the heuristic principles described earlier and along the lines of the flow diagram shown in Fig. 32 can be developed, leading ultimately to the implementation of useful scale-up criteria. Along the way, computer simulations, generated from the analysis of the concentration-time... 

The initial ACR experimental program proposed to test the scale-up criteria called for the construction of a 50 MM lb ethylene/year prototype reactor with its associated downstream gas processing facilities. This scale was originally thought to be the minimum size needed to assure the smooth start-up of a world-scale olefin plant. When the technology and economics of this proposed ACR plant were examined, the cost of the total facility was found to be extremely high. 

Evangelista, J. J., Katz, S., and Shinnar, R., Scale-up criteria for stirred tank reactors. AlChE J. 15,843 (1969). 

Podgorska and Bafdyga [Chem. Eng. Sci, 56, pp. 741-746 (2001)] present a model of drop breakage and coalescence and compare four scale-up criteria for agitated liquid-liquid dispersions ... 

The yield of secondary metabolites in a large-scale fermenter typically ranges from 0.1 to lOg/L of broth. Such poor yield leads to cumbersome and expensive processes for both product separation and broth disposal. Within the last decade, several novel bioreactors have been developed for the intensification of fermentation processes. Examples include a centrifugal bioreactor, a rotating packed bed fermenter, and a sonobioreactor. Most of these, however, are yet to be implemented on a production scale because they generally lack practicality and well-defined scale-up criteria. 

Final Discussion from the Viewpoint of the Dimensional Analysis No industrial stirring operation in Germany in connection with the scale-up criterion has caused more stir and none was more controversially discussed than the suspension of solid particles. It is noteworthy that the authors without exception ascribed to dimensional analysis the blame for the inappropriate or deficient, in the sense of scale-up criteria, at any rate inadequate pi space. 

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